Question

I need help on this practice problem It asks to solve the logarithmic equations. Number 3. And 4.

Answer 1

3) You have the following expression:

$\log _p4096=3$

In order to solve for p, proceed as follow:

- Use the property:

$\log _mn=\frac{\log n}{\log m}$

which applied to the given expression result:

$\frac{\log 4096}{\log p}=3$

- Next, solve for log p and take the complete equation as the exponent of a base 10:

$\begin{gathered} \log p=\frac{1}{3}\log 4096 \\ 10^{\log p}=10^{\frac{1}{3}\log 4096} \end{gathered}$

- By properties of logarithms you obtain:

$\begin{gathered} p=4096^{\frac{1}{3}}=\sqrt[3]{4096^{}} \\ p=16 \end{gathered}$